#16246: Add functions calculating all spanning trees, all bridges in a graph
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Reporter: jdickinson | Owner:
Type: enhancement | Status: new
Priority: major | Milestone: sage-6.2
Component: graph theory | Keywords: bridge, spanning tree
Merged in: | Authors: jdickinson
Reviewers: | Report Upstream: N/A
Work issues: | Branch:
Commit: | Dependencies:
Stopgaps: |
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This patch adds
1) a function that finds all spanning trees in a graph.
(adapted from "Bounds on Backtrack Algorithms for Listing Cycles, Paths,
and Spanning Trees" R. C. Read and R. E. Tarjan, 1975)
2) a function that finds all bridges in a graph recursively, that is used
in calculating the spanning trees
(adapted from the solution to 4.1.36 in Sedgewick's _Algorithms_ 4th ed.)
For example:
sage: G = Graph([(1,2),(1,2),(1,3),(1,3),(2,3),(1,4)])
sage: G.spanning_trees()
[Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices,
Graph on 4 vertices]
sage: len(G.spanning_trees()) == G.spanning_trees_count()
True
sage: G.bridges()
[(1, 4, None)]
These functions will assist in the calculation of the Jones polynomial of
a knot.
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Ticket URL: <http://trac.sagemath.org/ticket/16246>
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